1327 
EN CEN 
=ala) TK 
where we must remark that the first term may be omitted. Indeed, 
whatever be the value of 
OT 
a 
it certainly will be determined by the state of the body and its 
variations will therefore be limited to small changes on both sides 
of a certain mean value when the state is stationary. Then, however, 
7 
brt 
the mean value of the differential coefficient =(5-) taken over a 
q 
time of sufficient length, will be equal to zero. We hardly need 
remark that it is such a mean value of the pressure p and there- 
fore of the force Q, which we want to find. 
So we may write 
OD Ou. 
on aE Gar 
and, as we are seeking the value for the case g = 0, =) we 
may directly introduce this latter value into 7 and confine ourselves 
to terms with the first power of q when we represent U by a series. 
By putting q —0, the points P, P',... of which we spoke in § 2 
become immovable, so that we shall find the velocities of the par- 
ticles by differentiating with respect to the time their deviations 
E, 4,6, &',7',¢'... from the positions P, P’,... As now the coefficients uv, 8, 7 
in equations (3) are constants, the coordinate q does not appear 
in the expressions for the velocities and neither in 7. This leads to 
a further simplification, viz. 
ae 
0,U 
Oena vande ea 
$ 4. If, in the series for the potential energy, we confine our- 
selves, as we did in $ 1, to the terms that are of the second order 
with respect to 9,,9,---Qs, we may put 
U = $(a,9," + 429.7 +++ + asgs) H(A, + A, HA) - (6) 
It is evident that the first term, which is to represent the poten- 
tial energy for qg—=0,- must be the expression (1). Further A, is 
a constant, A, a homogeneous linear function of the coordinates 
Gy Ja -+++ Gs and A, a homogeneous quadratic function of these 
same variables. 
We have therefore, by (5) 
